The following picture shows two vectors as well as the parallelogram that is spanned by them.
The area of a parallelogram is simply the length times the height. In this
case, the length of the parallelogram is 
and the height is
. Thus, the area is 
. Very often it is helpful to think of
the area as a vector. The magnitude of the area vector is simply the ordinary
area. Its direction is perpendicular to the surface itself. Thus, the area
vector for the parallelogram above would point out of the screen.